Characterizing the Signless Laplacian H-Spectral Radius for Uniform Directed Hypergraphs

The importance of the signless Laplacian H-spectral radius is highlighted by its known links to connectivity and the maximum cut and independence number. In this paper, we establish signless Laplacian H-spectral radius bounds by simultaneously incorporating both pairwise and higher-order outdegree information. In contrast to the important estimates based solely on the maximum outdegree, our approach yields substantially improved bounds by leveraging richer structural parameters. We further introduce outdegree regularity and semiregularity, under which the tightness of the proposed bounds is fully characterized. Based on similarity transformations, we construct improved bounds using average two-outdegree data. These bounds reveal distinct behaviors between the adjacency and signless Laplacian H-spectral radius of directed hypergraphs. Numerical examples are provided to illustrate the effectiveness of these bounds.